41Axx Approximations and expansions

41A05 Interpolation [See also 42A15 and 65D05]
(1)

41A10 Approximation by polynomials (For approximation by trigonometric polynomials, see 42A10)
(1)

41A15 Spline approximation
(5)
 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol`skiïtype inequalities)
 41A20 Approximation by rational functions
 41A21 Padé approximation
 41A25 Rate of convergence, degree of approximation
 41A27 Inverse theorems
 41A28 Simultaneous approximation
 41A29 Approximation with constraints

41A30 Approximation by other special function classes
(3)

41A35 Approximation by operators (in particular, by integral operators)
(3)
 41A36 Approximation by positive operators
 41A40 Saturation
 41A44 Best constants
 41A45 Approximation by arbitrary linear expressions
 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
 41A50 Best approximation, Chebyshev systems

41A52 Uniqueness of best approximation
(1)

41A55 Approximate quadratures
(1)

41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
(3)

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
(1)

41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)
(1)
 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
 41A80 Remainders in approximation formulas
 41A99 None of the above, but in this section